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Sat, 10 Feb 2007 12:27:59 +0200Sat, 10 Feb 2007 12:27:59 +0200A piecewise analytical solution for Jiangs model of elastoplasticityhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1898
In this article, we present an analytic solution for Jiang's constitutive model of elastoplasticity. It is considered in its stress controlled form for proportional stress loading under the assumptions that the one-to-one coupling of the yield surface radius and the memory surface radius is switched off, that the transient hardening is neglected and that the ratchetting exponents are constant.Holger Lang; Klaus Dressler; Rene Pinnaureporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1898Tue, 02 Oct 2007 12:27:59 +0200A condition that a continuously deformed, simply connected body does not penetrate itselfhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1874
In this article we give a sufficient condition that a simply connected flexible body does not penetrate itself, if it is subjected to a continuous deformation. It is shown that the deformation map is automatically injective, if it is just locally injective and injective on the boundary of the body. Thereby, it is very remarkable that no higher regularity assumption than continuity for the deformation map is required. The proof exclusively relies on homotopy methods and the Jordan-Brouwer separation theorem.Holger Langreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1874Sat, 23 Jun 2007 13:31:37 +0200A homotopy between the solutions of the elastic and elastoplastic boundary value problemhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1776
In this article, we give an explicit homotopy between the solutions (i.e. stress, strain, displacement) of the quasistatic linear elastic and nonlinear elastoplastic boundary value problem, where we assume a linear kinematic hardening material law. We give error estimates with respect to the homotopy parameter.Holger Lang; Klaus Dressler; Rene Pinnau; Gerd Bitschreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1776Fri, 22 Sep 2006 16:05:14 +0200Error estimates for quasistatic global elastic correction and linear kinematic hardening materialhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1775
We consider in this paper the quasistatic boundary value problems of linear elasticity and nonlinear elastoplasticity with linear kinematic hardening material. We derive expressions and estimates for the difference of solutions (i.e. stress, strain and displacement) of both models. Further, we study the error between the elastoplastic solution and the solution of a postprocessing method, that corrects the solution of the linear elastic problem in order to approximate the elastoplastic model.Holger Lang; Klaus Dressler; Rene Pinnau; Michael Speckertreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1775Thu, 21 Sep 2006 20:54:30 +0200Lipschitz estimates for the stop and the play operatorhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1773
In this article, we give some generalisations of existing Lipschitz estimates for the stop and the play operator with respect to an arbitrary convex and closed characteristic a separable Hilbert space. We are especially concerned with the dependency of their outputs with respect to different scalar products.Holger Lang; Klaus Dressler; Rene Pinnaureporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1773Thu, 21 Sep 2006 12:05:33 +0200Parameter optimization for a stress-strain correction schemehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1702
A gradient based algorithm for parameter identification (least-squares) is applied to a multiaxial correction method for elastic stresses and strains at notches. The correction scheme, which is numerically cheap, is based on Jiang's model of elastoplasticity. Both mathematical stress-strain computations (nonlinear PDE with Jiang's constitutive material law) and physical strain measurements have been approximized. The gradient evaluation with respect to the parameters, which is large-scale, is realized by the automatic forward differentiation technique.Holger Lang; Rene Pinnau; Klaus Dreßlerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1702Sat, 21 Jan 2006 15:51:35 +0100A multiaxial stress-strain correction schemehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1701
A method to correct the elastic stress tensor at a fixed point of an elastoplastic body, which is subject to exterior loads, is presented and analysed. In contrast to uniaxial corrections (Neuber or ESED), our method takes multiaxial phenomena like ratchetting or cyclic hardening/softening into account by use of Jiang's model. Our numerical algorithm is designed for the case that the scalar load functions are piecewise linear and can be used in connection with critical plane/multiaxial rainflow methods in high cycle fatigue analysis. In addition, a local existence and uniqueness result of Jiang's equations is given.Holger Lang; Rene Pinnau; Klaus Dreßlerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1701Sat, 21 Jan 2006 15:51:16 +0100Algebraic Systems Theoryhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1567
Control systems are usually described by differential equations, but their properties of interest are most naturally expressed in terms of the system trajectories, i.e., the set of all solutions to the equations. This is the central idea behind the so-called "behavioral approach" to systems and control theory. On the other hand, the manipulation of linear systems of differential equations can be formalized using algebra, more precisely, module theory and homological methods ("algebraic analysis"). The relationship between modules and systems is very rich, in fact, it is a categorical duality in many cases of practical interest. This leads to algebraic characterizations of structural systems properties such as autonomy, controllability, and observability. The aim of these lecture notes is to investigate this module-system correspondence. Particular emphasis is put on the application areas of one-dimensional rational systems (linear ODE with rational coefficients), and multi-dimensional constant systems (linear PDE with constant coefficients).Eva Zerzreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1567Wed, 25 Aug 2004 09:34:44 +0200